{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "P\370\355klad 6" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "Naleznete obecne \+ reseni rovnice " }{TEXT 256 22 "y'' + 4y = 1/ sin(2x) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 43 "rovnice2:=diff(y(x),x$2)+4*y(x)=1/sin(2*x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)rovnice2G/,&-%%diffG6$-%\"yG6#%\"xG -%\"$G6$F-\"\"#\"\"\"*&\"\"%F2F*F2F2*&F2F2-%$sinG6#,$F-F1!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Vypocteme koreny charakteristicke \+ rovnice." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "read \"difproc. m\": solve(char(lhs(rovnice2)=0,y(x)),lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$^#\"\"#^#!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "N alezneme obecne reseni prislusne homogenni rovnice pomoci procedury " }{TEXT 257 3 "hom" }{TEXT -1 31 ". Pomoci volitelneho parametru " } {TEXT 260 6 "\"fund\"" }{TEXT -1 103 " nechame zobrazit take fundament alni system zadane rovnice, ktery budeme potrebovat pri dalsim vypoctu ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "ob_res_hom:=hom(lhs(ro vnice2)=0,y(x),\"fund\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$-%$sinG 6#,$%\"xG\"\"#-%$cosGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+ob_res_h omG/-%\"yG6#%\"xG,&*&&%\"cG6#\"\"\"F/-%$sinG6#,$F)\"\"#F/F/*&&F-6#F4F/ -%$cosGF2F/F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Partikularni res eni nehomogenni rovnice budeme hledat v nasledujicim tvaru." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "tvar:=y(x)=subs(c[1]=K[1](x) ,c[2]=K[2](x),rhs(ob_res_hom));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%% tvarG/-%\"yG6#%\"xG,&*&-&%\"KG6#\"\"\"F(F0-%$sinG6#,$F)\"\"#F0F0*&-&F. 6#F5F(F0-%$cosGF3F0F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 133 "Tak, ja k je v praktickem vypoctu obvykle, vynechame odvozeni a prejdeme rovno u k soustave rovnic pro prvni derivace neznamych funkci " }{XPPEDIT 18 0 "K[1](x);" "6#-&%\"KG6#\"\"\"6#%\"xG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "K[2](x);" "6#-&%\"KG6#\"\"#6#%\"xG" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "podminka1:=diff(K[1](x),x)*fund[1]+ diff(K[2](x),x)*fund[2]=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*podmi nka1G/,&*&-%%diffG6$-&%\"KG6#\"\"\"6#%\"xGF1F/-%$sinG6#,$F1\"\"#F/F/*& -F)6$-&F-6#F6F0F1F/-%$cosGF4F/F/\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "podminka2:=diff(K[1](x),x)*diff(fund[1],x)+diff(K[2]( x),x)*diff(fund[2],x)=rhs(rovnice2);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%*podminka2G/,&*&-%%diffG6$-&%\"KG6#\"\"\"6#%\"xGF1F/-%$cosG6#,$F1 \"\"#F/F6*(F6F/-F)6$-&F-6#F6F0F1F/-%$sinGF4F/!\"\"*&F/F/F=F?" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "Vyresime danou soustavu, ve ktere \+ pro jednoduchost oznacime prvni derivace hledanych funkci " }{XPPEDIT 18 0 "K[1](x);" "6#-&%\"KG6#\"\"\"6#%\"xG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "K[2](x);" "6#-&%\"KG6#\"\"#6#%\"xG" }{TEXT -1 9 " symboly " } {TEXT 259 4 "A, B" }{TEXT -1 2 ". " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "konst_der:=solve(subs(diff(K[1](x),x)=A,diff(K[2](x) ,x)=B,\{podminka1,podminka2\}),\{A,B\}); assign(konst_der);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*konst_derG<$/%\"BG#!\"\"\"\"#/%\"AG,$*&-% $cosG6#,$%\"xGF*\"\"\"-%$sinGF1F)#F4F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Intregraci dostaneme hledane funkce " }{XPPEDIT 18 0 "K[1 ](x);" "6#-&%\"KG6#\"\"\"6#%\"xG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "K[2 ](x);" "6#-&%\"KG6#\"\"#6#%\"xG" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "konst1:=int(A,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'konst1G,$-%#lnG6#-%$sinG6#,$%\"xG\"\"##\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "konst2:=int(B,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'konst2G,$%\"xG#!\"\"\"\"#" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "Upravime vyjadreni prvni konstanty uzavrenim argumentu logaritmu do absolutni hodnoty." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "konst1upr:=1/4*ln(abs(sin(2*x)));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%*konst1uprG,$-%#lnG6#-%$absG6#-%$sin G6#,$%\"xG\"\"##\"\"\"\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Vy jadrime obecne reseni nehomogenni rovnice." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 81 "ob_reseni:=y(x)=rhs(ob_res_hom)+subs(K[1](x)=konst1 upr,K[2](x)=konst2,rhs(tvar));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*o b_reseniG/-%\"yG6#%\"xG,**&&%\"cG6#\"\"\"F/-%$sinG6#,$F)\"\"#F/F/*&&F- 6#F4F/-%$cosGF2F/F/*(#F/\"\"%F/-%#lnG6#-%$absG6#F0F/F0F/F/*&#F/F4F/*&F )F/F8F/F/!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Vysledek muzeme overit pouzitim procedury " }{TEXT 258 8 "varconst" }{TEXT -1 126 ", \+ ktera automatizuje predchozi postup pomoci Mapleovskeho programovaciho jazyka.Rozdil je pouze v pridane absolutni hodnote. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "varconst(rovnice2,y(x)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(overeniG/-%\"yG6#%\"xG,**&&%\"cG6#\"\"\"F /-%$sinG6#,$F)\"\"#F/F/*&&F-6#F4F/-%$cosGF2F/F/*(#F/\"\"%F/F0F/-%#lnG6 #F0F/F/*&#F/F4F/*&F8F/F)F/F/!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Vykreslime nektera partikularni reseni pro pevnou hodnotu konstant y " }{XPPEDIT 18 0 "c[1] = 0;" "6#/&%\"cG6#\"\"\"\"\"!" }{TEXT -1 1 ". 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